Let x and y be real numbers satisfying 4x^2+5y^2=1. Over all such pairs, let the maximum and minimum values of 2x^2+3xy+2y^2 be M and N respectively. If M+N+MN=a/b, where a and b are coprime positive integers, what is the value of …

Let a be a real number and let m, n be natural numbers such that m < n. Prove that if 0 < a < 1 --> a^n < a^m < 1. So, what I thought to start was: since 0 < a 0 < a^n Also a < 1, a^n < 1. By the property …